Problem: What do the following two equations represent? $-4x+4y = 5$ $-12x+12y = 5$
Explanation: Putting the first equation in $y = mx + b$ form gives: $-4x+4y = 5$ $4y = 4x+5$ $y = 1x + \dfrac{5}{4}$ Putting the second equation in $y = mx + b$ form gives: $-12x+12y = 5$ $12y = 12x+5$ $y = 1x + \dfrac{5}{12}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.